https://doi.org/10.1140/epjb/s10051-024-00750-z
Topical Review - Statistical and Nonlinear Physics
Fractality in resistive circuits: the Fibonacci resistor networks
1
Instituto de Física, Universidade Federal de Catalão, CEP 13560-970, Catalão, GO, Brazil
2
Instituto de Física, Universidade Federal Fluminense, CEP 24210-340, Niterói, RJ, Brazil
3
Instituto de Física, Universidade de Brasília, 70910-900, Brasília, DF, Brazil
a
petrus@ufcat.edu.br
c
david888azv@gmail.com
Received:
27
May
2024
Accepted:
11
July
2024
Published online:
13
August
2024
We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network’s equivalent resistance converges uniformly in the parameter 
, where 
and 
are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.
Petrus H. R. dos Anjos, Fernando A. Oliveira, and David L. Azevedo contributed equally to this work.
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